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Eigenvalues And Weights Of Induced Subgraphs

by C. Delorme , 1999
"... We apply eigenvalue techniques for cut evaluation to produce relations between the weight and order of induced subgraphs, and apply these results to bound the stability number. ..."
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We apply eigenvalue techniques for cut evaluation to produce relations between the weight and order of induced subgraphs, and apply these results to bound the stability number.

Eigenvalue conditions for induced subgraphs

by J Harant , J Niebling , S Richter
"... Abstract Necessary conditions for an undirected graph G to contain a graph H as induced subgraph involving the smallest ordinary or the largest normalized Laplacian eigenvalue of G are presented. ..."
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Abstract Necessary conditions for an undirected graph G to contain a graph H as induced subgraph involving the smallest ordinary or the largest normalized Laplacian eigenvalue of G are presented.

Induced Subgraphs of Johnson Graphs

by Ramin Naimi, Jeffrey Shaw , 2006
"... The Johnson graph J(n, N) is defined as the graph whose vertices are the nsubsets of the set {1, 2, · · · , N}, where two vertices are adjacent if they share exactly n−1 elements. Unlike Johnson graphs, induced subgraphs of Johnson graphs (JIS for short) do not seem to have been studied before. W ..."
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The Johnson graph J(n, N) is defined as the graph whose vertices are the nsubsets of the set {1, 2, · · · , N}, where two vertices are adjacent if they share exactly n−1 elements. Unlike Johnson graphs, induced subgraphs of Johnson graphs (JIS for short) do not seem to have been studied before

Induced Subgraphs With Distinct Sizes

by Noga Alon, A. V. Kostochka , 2009
"... We show that for every 0 <ɛ<1/2, there is an n0 = n0(ɛ) such that if n> n0 then every n-vertex graph G of size at least ɛ ( ) () n n and at most (1 − ɛ) contains induced k-vertex 2 2 subgraphs with at least 10−7k different sizes, for every k ≤ ɛn. This is best possible, up to a constant 3 ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
We show that for every 0 <ɛ<1/2, there is an n0 = n0(ɛ) such that if n> n0 then every n-vertex graph G of size at least ɛ ( ) () n n and at most (1 − ɛ) contains induced k-vertex 2 2 subgraphs with at least 10−7k different sizes, for every k ≤ ɛn. This is best possible, up to a constant

Detecting induced subgraphs

by Benjamin Leveque, David Y. Lin, Frédéric MAFFRAY , Nicolas Trotignon , 2007
"... An s-graph is a graph with two kinds of edges: subdivisible edges and real edges. A realisation of an s-graph B is any graph obtained by subdividing subdivisible edges of B into paths of arbitrary length (at least one). Given an s-graph B, we study the decision problem ΠB whose instance is a graph ..."
Abstract - Cited by 13 (5 self) - Add to MetaCart
G and question is “Does G contain a realisation of B as an induced subgraph?”. For several B’s, the complexity of ΠB is known and here we give the complexity for several more. Our NP-completeness proofs for ΠB’s rely on the NP-completeness proof of the following problem. Let S be a set

Sizes of induced subgraphs of Ramsey graphs

by Noga Alon, József Balogh, Alexandr Kostochka, Wojciech Samotij , 2008
"... An n-vertex graph G is c-Ramsey if it contains neither a complete nor an empty induced subgraph of size greater than c log n. Erdős, Faudree and Sós conjectured that every c-Ramsey graph with n vertices contains Ω(n 5/2) induced subgraphs any two of which differ either in the number of vertices or i ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
An n-vertex graph G is c-Ramsey if it contains neither a complete nor an empty induced subgraph of size greater than c log n. Erdős, Faudree and Sós conjectured that every c-Ramsey graph with n vertices contains Ω(n 5/2) induced subgraphs any two of which differ either in the number of vertices

Line Graphs and Forbidden Induced Subgraphs

by Hong-jian Lai, Lubomír Soltés , 2001
"... Beineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, S8 oltes gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases. A graph is said to be a dumbbell if it cons ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
Beineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, S8 oltes gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases. A graph is said to be a dumbbell

Excluding induced subgraphs

by Maria Chudnovsky, Paul Seymour
"... ..."
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Induced subgraphs of prescribed size

by Noga Alon, Michael Krivelevich, Benny Sudakov
"... ..."
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Abstract not found

Induced Subgraphs of Given SIzes

by Paul Erdős, Zoltán Füredi, Bruce L. Rothschild, Vera T. Sós , 1998
"... We say (n, e) → (m, f), an (m, f) subgraph is forced, if every n-vertex graph of size e has “ an m-vertex spanned subgraph with f edges. For example, as Turán proved, (n, e) → for e> tk−1(n) and (n, e) ̸→, otherwise. We give a number of k, ` k 2 k, ` k 2 constructions showing that forced pairs ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
We say (n, e) → (m, f), an (m, f) subgraph is forced, if every n-vertex graph of size e has “ an m-vertex spanned subgraph with f edges. For example, as Turán proved, (n, e) → for e> tk−1(n) and (n, e) ̸→, otherwise. We give a number of k, ` k 2 k, ` k 2 constructions showing that forced
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